FMG and ASP conceived and designed the experiments, analyzed the data, contributed reagents/materials/analysis tools, and wrote the paper. FMG performed the experiments.
The authors have declared that no competing interests exist.
Angiogenesis (neovascularization) plays a crucial role in a variety of physiological and pathological conditions including cancer, cardiovascular disease, and wound healing. Vascular endothelial growth factor (VEGF) is a critical regulator of angiogenesis. Multiple VEGF receptors are expressed on endothelial cells, including signaling receptor tyrosine kinases (VEGFR1 and VEGFR2) and the nonsignaling co-receptor Neuropilin-1. Neuropilin-1 binds only the isoform of VEGF responsible for pathological angiogenesis (VEGF165), and is thus a potential target for inhibiting VEGF signaling. Using the first molecularly detailed computational model of VEGF and its receptors, we have shown previously that the VEGFR–Neuropilin interactions explain the observed differential effects of VEGF isoforms on VEGF signaling in vitro, and demonstrated potent VEGF inhibition by an antibody to Neuropilin-1 that does not block ligand binding but blocks subsequent receptor coupling. In the present study, we extend that computational model to simulation of in vivo VEGF transport and binding, and predict the in vivo efficacy of several Neuropilin-targeted therapies in inhibiting VEGF signaling: (a) blocking Neuropilin-1 expression; (b) blocking VEGF binding to Neuropilin-1; (c) blocking Neuropilin–VEGFR coupling. The model predicts that blockade of Neuropilin–VEGFR coupling is significantly more effective than other approaches in decreasing VEGF–VEGFR2 signaling. In addition, tumor types with different receptor expression levels respond differently to each of these treatments. In designing human therapeutics, the mechanism of attacking the target plays a significant role in the outcome: of the strategies tested here, drugs with similar properties to the Neuropilin-1 antibody are predicted to be most effective. The tumor type and the microenvironment of the target tissue are also significant in determining therapeutic efficacy of each of the treatments studied.
Neuropilin is a co-receptor for some of the isoforms of the vascular endothelial growth factor (VEGF) family. The presence of Neuropilin on endothelial or other cells increases binding of these isoforms to their signaling receptor VEGFR2, thus increasing pro-angiogenesis signaling and stimulating vascular growth. Neuropilin is thus a suitable target for anti-angiogenesis therapy, which holds promise for the treatment of vasculature-dependent diseases such as cancer and diabetic retinopathy. In this study, Mac Gabhann and Popel perform computational simulations of VEGF transport in breast cancer, using a previously validated model of VEGF–VEGF receptor interactions, as well as geometrical information on the tumor itself—tumor cells, vasculature, and extracellular matrix. Three different molecular therapies targeting Neuropilin are tested in silico, and the simulations predict that one of these therapies will be effective at reducing VEGFR2 signaling in certain types (or subtypes) of tumors, while the others will not. Thus, we demonstrate that identification of a target molecule is not sufficient; different therapeutic strategies targeting the same molecule may result in different outcomes.
Angiogenesis (neovascularization), the growth of new blood microvessels from preexisting microvasculature, is a critical physiological process for the growth of developing organs and during wound healing, ovulation, and pregnancy. Coronary or peripheral ischemia may be relieved by inducing angiogenesis [
Vascular endothelial growth factor (VEGF) is a family of secreted glycoproteins and critical regulators of angiogenesis [
(A) Schematic of the in vivo model. Parenchymal cells secrete VEGF; VEGF121 is freely diffusible, but VEGF165 can be sequestered by proteoglycans in the ECM (light gray) and the basement membranes (dark gray). The isoforms bind to VEGF receptors on the endothelial cells.
(B) VEGF isoforms bind to VEGFR2 that transduces the angiogenic signal intracellularly. VEGF121 does not bind Neuropilin-1; VEGF165 may bind both VEGFR2 and Neuropilin-1 simultaneously. Thus there are two pathways for the binding of VEGF165 to the signaling VEGFR2 receptor: first by binding directly, and second by binding Neuropilin-1 and then diffusing laterally on the cell surface to couple to VEGFR2. VEGFR1, which modulates the signaling of VEGFR2, binds both isoforms of VEGF. VEGFR1 also binds directly to Neuropilin-1. This complex is permissive for VEGF121–VEGFR1 binding but not VEGF165–VEGFR1; thus, high levels of Neuropilin-1 displace VEGF165 from VEGFR1, making it available for VEGFR2 binding. Only VEGF165 binds directly to the ECM binding site (represented by GAG chains).
(C) By targeting Neuropilin-1, we can target specifically VEGF165-induced signaling. Three methods for targeting Neuropilin-1 are analyzed here: blockade of Neuropilin-1 expression (e.g., using siRNA); blockade of VEGF–Neuropilin binding (e.g., using a fragment of placental growth factor to occupy the binding site); and blockade of VEGFR–Neuropilin coupling (e.g., using an antibody for Neuropilin-1 that does not interfere with VEGF–Neuropilin binding).
In previous work [
Three methods for targeting the VEGF165–Neuropilin interaction are modeled here. First, a blockade of Neuropilin-1 expression may be induced by use of siRNA or other methods to prevent the synthesis of the protein in the cells. Second, a protein that occupies the VEGF binding site on Neuropilin-1 can compete with VEGF165 for binding to that receptor. An example is a fragment of the placental growth factor isoform PlGF2. Full-length PlGF2 (a VEGF homolog) binds Neuropilin-1 and VEGFR1 (but not VEGFR2) [
This is the first computational model to our knowledge to include the interactions of the VEGF family and their receptors explicitly and in biophysical detail. The model includes the kinetics of all ligand–receptor interactions, which allows us to examine both short-term and long-term behavior of the system. All the parameters for the model have been obtained from previously published experimental data. Analysis of characteristic parameters shows that the kinetics of VEGF interactions are slower than the diffusion process, so diffusion is assumed to be fast, and we construct a compartmental model (i.e., spatial gradients of VEGF are not considered) with parenchymal cells secreting VEGF into the interstitial space and VEGF binding to receptors on the endothelial cell surface (
The geometrical parameters of the tissue under investigation here (breast tumor) are also incorporated into the model: interstitial space, tumor cell volume and surface area, microvessel volume and surface area. Changes to these parameters would result in changes to the kinetic parameters and concentrations in the model. The results presented here are therefore tissue-specific, but the model may be applied to other tissues.
VEGFR2 is the primary signaling receptor for VEGF, and we first analyze the results of the model for a tissue in which the endothelial cells express VEGFR2 and Neuropilin-1, but not VEGFR1; the effect of VEGFR1 is considered later. Initially, the system is in a steady state, as VEGF is secreted by the parenchymal cells and internalized by the endothelial cells, resulting in a flux through the interstitial space and the ECM (
We constructed a computational model of VEGF transport and interactions with its receptors in tumor tissue in vivo. The interstitial space between the tumor cells and the blood vessels is divided into three regions: the ECM, and the two basement membranes surrounding the tumor cells and the blood vessel endothelial cells (TBM and EBM, respectively). VEGF is secreted by the tumor cells and binds to cell surface receptors on the endothelial cells. In the case of VEGF165, it may also be sequestered by VEGF binding sites in the ECM and basement membranes. This sequestered VEGF can serve as a reservoir to buffer dynamic changes in free VEGF concentration. The binding interactions between VEGF121, VEGF165, and the receptors VEGFR1, VEGFR2, and Neuropilin-1 are shown in
(A) VEGF121 binds to VEGFR2 but not Neuropilin-1. VEGF165 binds both receptors as well as GAG chains in the interstitial space. VEGF165 bound to Neuropilin-1 can diffuse laterally on the cell membrane and bind VEGFR2 (and vice versa), coupling these receptors together, even though the receptors themselves do not interact.
(B) VEGF121 and VEGF165 both bind VEGFR1. Neuropilin-1 and VEGFR1 interact directly, forming a complex that is permissive for VEGF121 binding but not VEGF165.
(C) Inhibition of Neuropilin-1 expression results in a decrease in the insertion rate of Neuropilin receptors into the cell membrane (sN).
(D) PlGF2Δ, a fragment of placental growth factor, competes with VEGF165 for the binding site on Neuropilin-1.
(E) An antibody to Neuropilin-1 that does not interfere with VEGF165 binding can block the coupling of VEGF165–Neuropilin to VEGFR2, resulting in sequestration of VEGF on nonsignaling Neuropilin.
The signaling ligand–receptor complexes formed by VEGF121, VEGF165, and their receptors are shown in
One of three Neuropilin-targeting therapies is used and the system is observed for 48 hours. The first modification of Neuropilin expression is a change in the value of sN, the insertion rate of Neuropilin into the membrane (
As described in the introduction, PlGF2Δ is a fragment of placental growth factor that binds only to the VEGF165 binding sites of Neuropilin (
The antibody to Neuropilin being investigated here does not affect VEGF binding to Neuropilin [
The parameters required for simulation of this model fall into three categories: geometric, kinetic rates, and initial concentrations; they are given in
Microgeometrical Parameters for Breast Cancer
Kinetic Parameters of VEGF System
VEGF Concentration and VEGFR Density
The model is applicable to any solid tumor. To be specific, in this study we use the geometric parameters typical for breast cancer as summarized in
The average extracellular fluid volume in breast tumors has been measured from 51%–63% [
The vascular density appears to range widely for breast cancer, with 100–500 capillaries/mm2 cross-sectional area of tissue measured in different tumor samples [
(A–C) The time course of VEGF–VEGFR2 complex formation on the endothelial cells following each of the three treatments. For blocking VEGF–Neuropilin-1 binding (B) and VEGFR–Neuropilin-1 coupling (C), this figure represents bolus intratissue protein delivery at time 0. For Neuropilin-1 expression blockade, insertion of Neuropilin-1 into the membrane decreases to the indicated level at time 0. The VEGF121–VEGFR2 binding curve is indistinguishable from the no-treatment line in each case. The tumor modeled here expresses 10,000 VEGFR2 and 100,000 Neuropilin per endothelial cell.
(D–F) Free (unbound) VEGF concentration in the interstitial space. *VEGF121 secreted at the same rate as VEGF165.
(G–I) The concentration of VEGF inhibitor in the interstitial space, or density of Neuropilin, on the blood vessel endothelial cell surface.
The 2% vascular volume gives us an interstitial volume of 58% cm3/cm3, and having fixed the total vascular volume and the size of each vessel, the volume taken up by the endothelial cells of the microvessels is determined to be 0.4% cm3/cm3 based on 0.5 μm thickness. The remaining tissue volume (39.6%) is occupied by the cancer cells.
From the relative volumes of each of the extracellular regions, and the surface areas of the vessels and tumor cells, we can calculate the total surface area of all vessels and tumor cells per unit volume of tissue. For the above parameters, they are 105 cm2 endothelial cell surface / cm3 tissue and 1,534 cm2 tumor cell surface / cm3 tissue.
Last, both the vessels and the tumor cells have associated basement membranes. The thickness of these was not available for breast cancer, and we have assumed thickness of 50 nm and 30 nm, which are within the range of thicknesses of basement membranes observed in other tissues [
The average inhibition of VEGF–VEGFR2 complex formation over the 48 hours following blockade of Neuropilin-1 expression (A), or bolus intratissue protein delivery (B) of competitive binding inhibitor or VEGFR–Neuropilin-1 coupling blocker. Endothelial cells expressing 10,000 VEGFR2 and 100,000 Neuropilin-1.
The kinetic rates for VEGF isoform binding to and unbinding from VEGF receptors and Neuropilins are based on experimental measurements and are similar to those used in previous models [
(A–C) Formation of VEGF–VEGFR2 complexes over time following anti-Neuropilin treatment, for a tumor expressing 10,000 VEGFR1 per endothelial cell in addition to the VEGFR2 and Neuropilin-1 expression of
(D–F) VEGF–VEGFR1 complex formation.
(G–I) Free (unbound) interstitial VEGF concentration. *VEGF121 secreted at the same rate as VEGF165.
The initial concentration of unbound VEGF has been determined by microdialysis of breast tumors to be in the range 20–70 pg/ml, or 0.5–1.5 pM [
Endothelial cells expressing 10,000 VEGFR1, 10,000 VEGFR2, and 100,000 Neuropilin-1.
For the set of ordinary differential equations above, concentrations are expressed in per-tissue-volume units. That is, interstitial concentrations are expressed as pmol/(cm3 tissue) rather than pM; pM in this case would be equivalent to pmol/(liter of interstitium). Surface concentrations are similarly expressed as pmol/(cm3 tissue) rather than per-surface-area units such as molecules/cell or pmol/(cm2 cell surface area). All of these units may be interconverted using the tissue's characteristic geometrical parameters as described in the legend of
For the equations to hold, the units of the parameters used in the equations must also be changed to be consistent, e.g., the units of
Tissues that express low levels of Neuropilin-1 are insensitive to all Neuropilin-targeting treatments. The inhibition of VEGF–VEGFR2 signaling is directly proportional to Neuropilin-1 density (A–C), except at very high Neuropilin levels, which can overcome the inhibition. Tissues that express intermediate and high levels of Neuropilin-1 are further distinguished by the level of expression of VEGFR1. Blocking VEGFR–Neuropilin coupling is the most effective treatment to reduce VEGF–VEGFR2 signaling for tissues with any VEGFR1 expression level. However, in high VEGFR1 tissues, the other treatments are also quite effective. All three treatments significantly induce VEGF–VEGFR1 complex formation (D–F). The circles in each figure denote the conditions for
Simulations of VEGF transport in breast cancer, and of therapeutic interventions to inhibit signaling, were developed as described in the Methods section. The simulations are first presented with the endothelial cells of the blood vessels expressing VEGFR2 and Neuropilin but not VEGFR1. We will then examine the impact of VEGFR1 co-expression.
Blockade of Neuropilin-1 synthesis results in a gradual decline in Neuropilin expression on the endothelial cell surface (
(A–C) VEGF–VEGFR2 complex formation on the endothelial cells following each of the three treatments. The tumor modeled here expresses 10,000 VEGFR2 and 100,000 Neuropilin per endothelial cell. Gray lines represent the case of 2% vascular volume, as depicted in
(D–F) Free (unbound) VEGF concentration in the interstitial space. *VEGF121 secreted at the same rate as VEGF165.
(G–I) The concentration of VEGF inhibitor in the interstitial space, or density of Neuropilin on the blood vessel endothelial cell surface.
Blockade of VEGF–Neuropilin binding again results in a transient decrease in the binding of VEGF165 to VEGFR2 (
The gray lines represent the case of 2% vascular volume (as depicted in
Blockade of VEGFR–Neuropilin coupling results in significantly higher peak inhibition than the first two treatments: 80% at 1 μM of the Neuropilin-1 antibody (
Our computer simulations predict that the maximal average inhibition of VEGF–VEGFR2 complex formation over the 48 hours is less than 30% for Neuropilin-1 expression blocking or VEGF binding blocking, but close to 80% for blocking VEGFR–Neuropilin coupling (
While the blockade of VEGFR–Neuropilin coupling exhibits prolonged inhibition of VEGF–VEGFR2 binding (
Some tissues, but not all, also demonstrate VEGFR1 expression on endothelial cells. Unlike VEGFR2, VEGFR1 interacts directly with Neuropilin-1, and the complex formed can bind VEGF121 but not VEGF165 [
All three of the treatments now resulted in significant, sustained decreases in VEGF165−VEGFR2 signaling (
The result of functional Neuropilin-1 loss (by expression or binding blockade) is, as before, that VEGF165 signaling becomes similar to VEGF121 signaling. In tissues that express VEGFR1 (with or without Neuropilin), most VEGF121 binds to VEGFR1 (higher affinity than VEGFR2), and, thus, the VEGF121 signaling through VEGFR2 is decreased as the receptors compete for the available ligand. Blockade of VEGFR-Neuropilin coupling, on the other hand, results in a decrease in VEGFR2 signaling beyond that of VEGF121 (
The vasculature in different tissues—and in different tumors—expresses different amounts of each VEGF receptor. This can result in differing responses to therapies. The tissue-specific nature of these interactions is investigated by varying the receptor expression of both Neuropilin-1 and VEGFR1 (
It is important to note that for all endothelial cell types that have been measured, from various different tissues, cell surface VEGFR1 expression is equal to or less than VEGFR2 expression, which suggests that blocking receptor coupling will be the most effective treatment.
VEGF–VEGFR1 binding is increased by each Neuropilin treatment except for tissues expressing a high level of VEGFR1 and a low level of Neuropilin-1 (
The vascular volume varies significantly from tumor to tumor. Here we simulate a tissue in which the vessels occupy 5% of the tissue volume (the vascular space 4.2% of volume). For this simulation, the vessel surface area is 218 cm2/cm3, and the volume of the interstitial compartment is reduced slightly. The increased vascularity also increases the total volume of endothelial basement membrane. The increased vessel density results in increased receptor density in the tissue, and so the inhibitors are depleted more quickly (
The vasculature that invests a tumor has been recognized as a therapeutic target that can be exploited to starve the tumor or to increase the delivery of drugs directly to the tumor [
We have previously built a computational model that describes the behavior of the VEGF–VEGF receptor system [
Thus, the model shows that it is not enough to identify Neuropilin as a therapeutic target due to its specificity for VEGF165; different methods of targeting Neuropilin result in different outcomes.
It should be noted that here we define effectiveness as the decrease in VEGF–VEGFR2 binding over the 48 hours following treatment. Timing is a crucial component of intracellular signaling, and it is not clear at this point whether the prolonged inhibition of signaling (e.g.,
For VEGFR2, Neuropilin-1-expressing vasculature, inhibition of VEGF–Neuropilin-1 binding, or Neuropilin-1 expression blockade result in transient VEGFR2-signaling decrease, even though the inhibiting factor is not transient. Sustained high levels of the VEGF–Neuropilin-1 binding inhibitor (or sustained depletion of Neuropilin from the surface) in the interstitial space result in VEGF–VEGFR2 signaling recovering from the inhibition during the simulation due to the increasing interstitial VEGF concentration.
The vasculature in different types of breast cancer expresses different levels of VEGFR1, VEGFR2, and Neuropilin-1. In fact, the expression of these receptors may vary spatially within a tumor [
We have not included the effect of VEGF receptors on the tumor cells themselves. This is increasingly being identified as a source of autocrine survival and growth signaling for the tumor cells. We focused instead on the impact on pro-angiogenic signaling at the endothelial cell surface. Inclusion of VEGF receptors on the tumor cells would not qualitatively change our results. For example, the presence of Neuropilin on tumor cells would offer an alternate route for VEGF (away from the endothelial cells). Blockade of Neuropilin expression, or blocking VEGF–Neuropilin binding, would result in the VEGF that normally binds to tumor cells being redirected to the endothelial cells, possibly increasing pro-angiogenic signaling. By contrast, blockade of VEGFR–Neuropilin coupling would not have this problem, as VEGF165 could continue to bind the Neuropilin receptors on tumor cells and would not be displaced.
This model does not include pharmacokinetics—i.e., the route by which the drugs would get to the tumor. It is only concerned with their activity or efficacy once present at the tumor. As such, even for intratumoral injection, we assume that none of the inhibitor is lost to the bloodstream or lymphatics. Significant loss of this type from the interstitial space would decrease the efficacy of each of these inhibitors. In addition, vascular heterogeneity within a tumor is not addressed in this study.
This is the first computational model of VEGF transport in vivo, and the first molecularly detailed model of VEGF inhibition strategies. Models such as this can also be used to investigate other aspects of drug delivery, e.g., dosing and scheduling, as they deal with the site of action of the drug. Testable predictions of this model include the increase in interstitial VEGF concentration in response to the administration of each of the therapeutic strategies, as well as the characteristic signaling inhibition that could be detected at the level of receptor phosphorylation. These predictions should stimulate extensive experimental studies, and the model presented here would serve as a quantitative guide to experimental design.
For example, preclinical models of breast cancer could be used to test the therapeutic strategies and validate the model. Following characterization of breast cancer lines and their induced vasculature, VEGFR2–NRP1 and VEGFR2–VEGFR1–NRP1-expressing candidates would be selected for comparison (
Analogous to the drugs targeting Her2-positive breast cancer that are not effective against Her2-negative breast cancer [
Simulations of VEGF transport in human breast cancer were developed based on the model described in the Results section. The appropriate secretion rate for each simulation was used to achieve a steady state, free (unbound) VEGF concentration of 1pM. Then a therapeutic intervention was simulated by changing appropriate parameters or introducing new molecular species into the system. The complete set of coupled nonlinear ordinary differential equations (see
Accession numbers from UniProt (
endothelial cell basement membrane
extracellular matrix
tumor cell basement membrane
vascular endothelial growth factor
VEGF receptor tyrosine kinases